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Chapter 3: Problem 54

Plot the point in a coordinate plane. $$\mathrm{C}(5,0)$$

Short Answer

Expert verified
Point \( C(5,0) \) is located 5 units right of the origin, on the x-axis in the Cartesian plane.

Step by step solution

01

Identify x and y coordinates

The point given \(C(5,0)\) is an ordered pair. It indicates the position of the point C on a Cartesian plane. The first value, 5, corresponds to the x-coordinate, which defines the horizontal position of the point. The second value 0 is the y-coordinate, indicating the vertical position of the point. Here, the x-coordinate is 5 and the y-coordinate is 0.
02

Plot the Point on the Cartesian Plane

The next step is to plot the point on the Cartesian coordinate system. To do this, first locate the point along the x-axis that corresponds to the x-coordinate (5 in this case). Here point C is 5 units to the right of the origin on the x-axis. Then move vertically according to the y-coordinate (0 in this case), which means staying on the x-axis. Plot point C at this location.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Plotting Points
When you encounter an ordered pair like \((5,0)\), plotting it on a coordinate plane involves only a few steps. Each point on the Cartesian plane is defined by two numbers called coordinates.
Begin by identifying these two values, commonly referred to as the x-coordinate and y-coordinate.
  • The x-coordinate determines how far the point is positioned horizontally from the origin.
  • The y-coordinate determines the vertical placement relative to the origin.
For example, in the ordered pair \((5,0)\), the numbers tell you where to find the point on the plane. Start at the origin, move 5 units to the right along the x-axis. Since the y-coordinate is zero, no vertical movement is necessary.
Finally, mark the point at this exact location鈥攁 simple process, yet crucial for understanding the basics of graphing on a coordinate plane.
Cartesian Plane
The Cartesian plane is the foundation of graphing in mathematics. It consists of two perpendicular lines: the x-axis, which runs horizontally, and the y-axis, running vertically. These axes intersect at a central point called the origin, usually denoted as \((0,0)\).
  • The horizontal x-axis and vertical y-axis divide the plane into four quadrants, which are numbered counterclockwise.
  • The position of any point on the plane is determined by an ordered pair \((x, y)\).
Understanding how these axes work is essential for plotting points. Each coordinate value indicates direction and distance from the origin:
The x-coordinate tells you how many units to move left or right.
The y-coordinate tells you how many units to move up or down from the x-axis. This grid-like structure allows you to precisely determine locations and visualize mathematical equations easily.
Ordered Pairs
Ordered pairs are fundamental to understanding and working within the Cartesian plane. An ordered pair takes the form \((x,y)\), where each component of the pair plays a distinct role.
  • The first number in the pair represents the x-coordinate, indicating horizontal movement.
  • The second number is the y-coordinate, indicating vertical movement.
The significance of the "order" in ordered pairs cannot be overstated: changing the order changes the location of the point on the plane. For instance, the ordered pair \((2,3)\) points to a different location than \((3,2)\) in a coordinate system. Always ensure that you follow the format, moving first horizontally along the x-axis, then vertically along the y-axis. This systematic approach helps us accurately plot and interpret data visually.

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